Consider the following. 5 -2 0 0 1 -3 A = 0 -3 0 P = 0 4 -2 -2 2 1 2 2 (a) Verify that A is diagonalizable by computing P-1AP. p-lAP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (11, 12, 13) =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following.
5 -2 0
0 1 -3
A =
0 -3 0
P =
0 4
-2
-2 2
1 2
2
(a) Verify that A is diagonalizable by computing P-'AP.
p-1AP =
(b) Use the result of part (a) and the theorem below to find the eigenvalues of A.
Similar Matrices Have the Same Eigenvalues
If A and B are similar n x n matrices, then they have the same eigenvalues.
(^1, 12, 13) =
Transcribed Image Text:Consider the following. 5 -2 0 0 1 -3 A = 0 -3 0 P = 0 4 -2 -2 2 1 2 2 (a) Verify that A is diagonalizable by computing P-'AP. p-1AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (^1, 12, 13) =
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